## This content will become publicly available on April 22, 2020

## Geodesic interpolation for reaction pathways

## Abstract

The development of high throughput reaction discovery methods such as the *ab initio* nanoreactor demands massive numbers of reaction rate calculations through the optimization of minimum energy reaction paths. These are often generated from interpolations between the reactant and product endpoint geometries. Unfortunately, straightforward interpolation in Cartesian coordinates often leads to poor approximations that lead to slow convergence. In this work, we reformulate the problem of interpolation between endpoint geometries as a search for the geodesic curve on a Riemannian manifold. We show that the perceived performance difference of interpolation methods in different coordinates is the result of an implicit metric change. Accounting for the metric explicitly allows us to obtain good results in Cartesian coordinates, bypassing the difficulties caused by redundant coordinates. Using only geometric information, we are able to generate paths from reactants to products which are remarkably close to the true minimum energy path. In conclusion, we show that these geodesic paths are excellent starting guesses for minimum energy path algorithms.

- Authors:

- Stanford Univ., Stanford, CA (United States). Dept. of Chemistry and SLAC National Accelerator Lab

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1528918

- Grant/Contract Number:
- AC02-76SF00515; N00014-16-1-2557; N00014-17-1-2875

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 150; Journal Issue: 16; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

### Citation Formats

```
Zhu, Xiaolei, Thompson, Keiran C., and Martínez, Todd J. Geodesic interpolation for reaction pathways. United States: N. p., 2019.
Web. doi:10.1063/1.5090303.
```

```
Zhu, Xiaolei, Thompson, Keiran C., & Martínez, Todd J. Geodesic interpolation for reaction pathways. United States. doi:10.1063/1.5090303.
```

```
Zhu, Xiaolei, Thompson, Keiran C., and Martínez, Todd J. Mon .
"Geodesic interpolation for reaction pathways". United States. doi:10.1063/1.5090303.
```

```
@article{osti_1528918,
```

title = {Geodesic interpolation for reaction pathways},

author = {Zhu, Xiaolei and Thompson, Keiran C. and Martínez, Todd J.},

abstractNote = {The development of high throughput reaction discovery methods such as the ab initio nanoreactor demands massive numbers of reaction rate calculations through the optimization of minimum energy reaction paths. These are often generated from interpolations between the reactant and product endpoint geometries. Unfortunately, straightforward interpolation in Cartesian coordinates often leads to poor approximations that lead to slow convergence. In this work, we reformulate the problem of interpolation between endpoint geometries as a search for the geodesic curve on a Riemannian manifold. We show that the perceived performance difference of interpolation methods in different coordinates is the result of an implicit metric change. Accounting for the metric explicitly allows us to obtain good results in Cartesian coordinates, bypassing the difficulties caused by redundant coordinates. Using only geometric information, we are able to generate paths from reactants to products which are remarkably close to the true minimum energy path. In conclusion, we show that these geodesic paths are excellent starting guesses for minimum energy path algorithms.},

doi = {10.1063/1.5090303},

journal = {Journal of Chemical Physics},

number = 16,

volume = 150,

place = {United States},

year = {2019},

month = {4}

}